What does it mean for a set to be bounded?

  • Thread starter royzizzle
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  • #1
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what does it mean for a set to be bounded??

in the context of the hein-borel theorem

i mean the mathematically rigorous definition
 

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  • #2
Office_Shredder
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S a subset of Rn is bounded if there exists M>0 so that for all x in S, |x|<M
 
  • #3
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Another equivalent definition is that it has finite diameter, where

[tex]\mathrm{diam}(S) = \sup_{x, y \in S}(\mathrm{dist}(x, y)).[/tex]

This is applicable to any metric space (though the Heine-Borel theorem is not!).
 

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